Gauge and process for adjusting bearings

ABSTRACT

A setting gauge (G) determines the thickness of a spacer ( 22 ) which gives the correct setting for a pair of tapered roller bearings (B 1 , B 2 ) that are mounted in opposition to accommodate relative rotation between machine components (S, H). The gauge has a base ( 50 ) which at one end fits against a surface ( 12 ) to which the spacer is to be applied, and at its other end holds one of the races ( 32 ) of the bearing (B 2 ) remote from the other race ( 30 ) which remains in its operating position. In addition, the gauge has a pair of gauge elements ( 52, 54 ), one of which fits against a conical envelope along the remote race and the other of which fits against an identical conical envelope on the race which remains in its operating position, in effect, projecting the conical envelope defined by the in-place race out of the bearing to a remote location so that measurements may be taken from the bearing. The race which is remote during the measurements has a cylindrical surface ( 48 ) which is configured to fit another cylindrical surface ( 10 ) on one of the machine components (H) with an interference fit, and the gauge also measures the diameters of the two cylindrical surfaces so that the magnitude of the interference fit may be ascertained and its effect on the bearing compensated.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application derives and claims priority from U.S. provisionalapplication 60/266,790, filed Feb. 6, 2001, and from Internationalapplication PCT/US02/03979, filed Feb. 6, 2002.

TECHNICAL FIELD

This invention relates in general to antifriction bearings and, moreparticularly, to a gauge and a process for adjusting such bearings.

BACKGROUND ART

Wherever shafts rotate in housings one finds bearings of one type oranother to support such shafts. Single row tapered roller bearingsorganized in pairs and mounted in opposition perhaps function best in aninstallation of this type. These bearings carry heavy radial loads andthrust or axial loads as well. Being mounted in opposition, they can beadjusted against each other to varying conditions of end play orpreload. Too much end play concentrates loads in limited regions of thebearings and furthermore creates radial and axial clearances whichdetract from the stability of the shaft. Preload insures that the shaftwill rotate about a fixed axis and thus provides stability, but too muchpreload increases friction within the bearings and may lead to earlybearing failure. Thus, the adjustment of oppositely mounted bearingsagainst each other to achieve the proper setting represents an importantstep in the assembly of a shaft in a housing.

The typical tapered roller bearing has an inner race or cone, an outerrace or cup and a single row of tapered rollers located between racewayson the cone and cup. When two such bearings are mounted in opposition,either the small ends of the rollers in the two rows are presentedtoward each other (indirect mounting) or the large ends are presentedtoward each other (direct mounting). Irrespective of the arrangement,the bearings are adjusted by controlling the spacing between the cups ofthe two bearings or the spacing between the cones. Installing shims orspacers behind a cup or a cone in a bearing arrangement represents oneof the more common practices for controlling the spacing that determinesthe setting for the bearings.

Perhaps trial and error is the least complex procedure for determiningthe size of a shim or spacer, but this procedure lacks precision and ismore time consuming. More sophisticated procedures rely on measurements.Indeed, one procedure, in effect, projects surfaces out of a bearingwhere the distance between the surfaces is easily measured. From thesemeasurements one can select a shim that will provide a setting thatclosely proximates the desired setting.

But in the typical bearing arrangement having two single row taperedroller bearings factors other than the measurements taken from theprojected surfaces affect the setting. For example, an interference fitbetween the cylindrical exterior surface of a cup and the cylindricalhousing bore into which the cup fits will shrink the diameter of the cupraceway and thus change the width of the bearing. That in turn willalter the setting of the oppositely mounted bearings. The typicalprocedure for projecting surfaces takes the interference fit intoaccount only from the standpoint of the nominal dimensions for theinterfering cylindrical surfaces that produce the interference fit. Buttolerances in the outer diameter of a cup and in the bore into which itfits can vary the magnitude of the interference fit, and this in turnwill produce a variance from the desired setting for the bearings. To besure, the cylindrical surfaces may be measured separately, but thecomponents that make up the setting must be serialized and united atassembly.

SUMMARY OF THE INVENTION

The present invention resides in a setting gauge which in effectprojects a conical envelope out of one of two tapered roller bearingsthat are mounted in opposition, so that axial measurements may be madebetween the projected conical envelope and another and identical conicalenvelope that assumes its normal operating position, all for calculatingadjustments necessary to give the bearings the proper setting. The gaugealso measures the diameter of a cylindrical surface on a race thatcarries the projected envelope and also the diameter of anothercylindrical surface along which the race is to be installed with aninterference fit. It determines the change in bearing width caused bythe interference fit. The invention also resides in the gauge togetherwith inner and outer machine components on which it is installed to makethe measurements. In addition, the invention resides in the processutilized by the gauge.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a longitudinal sectional view of a shaft supported on bearingsadjusted with a gauge constructed in accordance with and embodying thepresent invention;

FIG. 2 is a sectional view of the housing and shaft with the gaugefitted to one of the bearings; and

FIG. 3 is an enlarged sectional view of the gauge.

BEST MODE FOR CARRYING OUT THE INVENTION

Referring now to the drawings (FIG. 1), a shaft S rotates in a housing Hon two tapered roller bearings B1 and B2 which establish the axis ofrotation X for the shaft S. The bearings B1 and B2 transfer radial loadsbetween the shaft S and housing H as well as thrust loads, the bearingB1 taking thrust loads in one axial direction and the bearing B2 in theother. The shaft S constitutes an inner machine component, whereas thehousing H constitutes an outer machine component.

At its one end the housing H contains (FIG. 1) a bore 2 which leads upto a shoulder 4. At the same end the shaft S has a bearing seat 6 whichleads up to a shoulder 8 that is presented toward the shoulder 4 in thehousing H. The bearing B1 fits into the bore 2 and around the seat 6. Atits opposite end the housing H contains a cylindrical through bore 10that opens out of a reference surface 12 which is recessed andperpendicular to the axis X. The shaft S at this end has a bearing seat14 which leads up to a shoulder 16 that is presented in the samedirection as the reference surface 12. The bearing B2 fits into the bore10 and around the seat 14. Whereas the shoulder 4 prevents the bearingB1 from moving out of its bore 2, the bearing B2 is confined to its bore10 by an annular retainer 18 that is secured to the housing H at thereference surface 12 with machine screws 20. Between the referencesurface 12 and the retainer 18 lies a spacer, such as a shim 22, havinga thickness t.

Each bearing B1 and B2 includes (FIG. 1) an inner race in the form of acone 30, an outer race in the form of a cup 32 that surrounds the cone30, and rolling elements in the form of tapered rollers 34 organized ina single row between the cone 30 and the cup 32. Each also has a cage 36which maintains the proper spacing between adjacent rollers 34. The cone30 has a tapered raceway 38 that is presented outwardly away from theaxis X and a thrust rib 40 at the large end of the raceway 38. Thethrust rib 40 leads out to a back face 42 that is squared off withrespect to the axis X. The cup 32 has a tapered raceway 44 that ispresented inwardly toward the raceway 38 of the cone 30. The raceway 44tapers downwardly to a back face 46 that is likewise squared off withrespect to the axis X. While the raceway 44 is presented inwardly, thecup 32 has a cylindrical exterior surface 48 that is presented outwardlyaway from the axis X. The tapered rollers 34 have tapered side facesalong which they contact the raceways 38 and 44, there being generallyline contact between the side faces and raceways 38 and 44. The rollers34 also have large end faces along which they contact the thrust rib 40.Indeed, the thrust rib 40 prevents the rollers 34 from moving up theraceways 38 and 44 and vacating the annular space between the raceways38 and 44. The rollers 34 are on apex, meaning that the conicalenvelopes in which the side faces of the rollers 34 lie have theirapices at a common point along the axis X as do the conical envelopesfor the raceways 38 and 44.

The cone 30 of the bearing B1 fits over the bearing seat 6 with aninterference fit and with its back face 42 against the shoulder 8 on theshaft S. The cup 32 of the bearing B1 fits into the bore 2 of thehousing H with an interference fit and with its back face 46 against theshoulder 4 at the end of the bore 2. The bearing B1 transfers radialloads between the shaft S and the housing H, and by reason of itstapered geometry, prevents the shaft S from moving farther toward theshoulder 4 in the housing H and away from the bearing B2.

The cone 30 of the bearing B2 fits over the other bearing seat 14 withan interference fit and with its back face 42 against the shoulder 16.The cup 32 of the bearing B2 fits into the through bore 10 with aninterference fit. Its back face 46 bears against the retainer 18, so theretainer 18 prevents the cup 32 of the bearing B2 from migrating out ofthe bore 10. The bearing B2 likewise transfers radial loads between theshaft S and housing H and by reason of its tapered geometry prevents theshaft S from moving in the opposite direction through the bore 10, thatis to say, farther toward the retainer 18 and away from the bearing B1.Thus, the two bearings B1 and B2 confine the shaft S in the housing,both radially and axially, yet enable the shaft S to rotate about theaxis X with minimal friction. The thickness t of the shim 22 determinesthe axial position of the cup 32 for the bearing B2 in the through bore10, and that in turn determines the setting for the two bearings B1 andB2.

After selecting the setting desired for the bearings B1 and B2, whetherit be end play or more likely preload, one determines the thickness t ofthe shim 22 from measurements derived from a setting gauge G (FIGS. 2and 3) that, in effect, projects the cup raceway 44 and back face 46axially beyond the cone 30 of the bearing B2. Actually, the gauge Gseparates two conical envelopes that coincide when the bearing B2 is inits operating condition, the one envelope being the tapered raceway 44of the cup 32 and the other being formed by the outwardly presentedsurfaces on the tapered rollers 34. One end of the gauge G fits into thethrough bore 10 of the housing H and around the rollers 34 of thebearing B2. At that end it also bears against the reference surface 12.At its other end the gauge G receives the cup 32 of the bearing B2 andhas the retainer 18 or a like retaining plate secured to it, althoughtemporarily. The gauge G includes an outer member or base 50 and twoinner members, namely a female element 52 and a male element 54, each ofwhich has the capacity to slide independently of each other within thebase 50. In addition, the gauge G has a measuring device 56, such as alinear variable differential transformer (LVDT), which is mounted on thefemale element 52 where it measures the distance between the two innerelements 52 and 54. Finally, the gauge G has a spring 58 which urges thetwo inner elements 52 and 54 apart with a light force.

The base 50, which resembles a sleeve, at one end is small enough to fitagainst the recessed reference surface 12 at the end of the through bore10 in the housing H. Here the base 50 is provided with an end face 60that is squared off with respect to the axis X. At its opposite end thebase 50 has another end face 62 which is likewise squared off withrespect to the axis X. The two end faces 60 and 62 lie a known distancea apart. Internally, the base 50 has a cylindrical end bore 64 whichopens out of the end face 62, it having a diameter that is slightlygreater than the diameter of the outer surface for the cup 32 of thebearing B2. Thus, the cup 32 of the bearing B2 will fit loosely into thebore 64. Moreover, the length of the end bore 64 exceeds the length ofthe cup 32, so that the bore 64 will receive the cup 32 in its entirety.The base 50 also contains a larger extended bore 66—actually acounterbore—which receives the two inner elements 52 and 54, with thefemale element 52 extending out to and beyond the end face 60 and themale element 54 extending into the end bore 64. At the ends of theextended bore 66, the base 50 has stops 68 which confine the innerelements 52 and 54 to the base 50. Finally, the base 50 has an airchannel 70 that leads to and opens into the end bore 64.

The female element 52 fits within the extended bore 66 such that it canslide to and fro in the bore 66, but with relatively little radialclearance. At one end, the female element 52 projects beyond the endface 60 of the base 50, and here it possesses a cylindrical externalsurface 76 that is slightly smaller in diameter than the through bore 10of the housing H. At this end, the female element 52 also has aninternal conical gauging surface 78 that opens out of the end where itis presented inwardly toward the axis X, its taper corresponding to thetaper of the conical envelope formed by the outer surfaces of therollers 34, which is the same as the taper of the raceway 44 for the cup32 of the bearing B2. In other words, the included angle between theconical surface 78 and the axis X corresponds to the included anglebetween the tapered raceway 44 and the axis X. At its other end, whichis within the bore 66 of the base 50, the female element 52 has an endplate 80. A fixed distance b exists between an arbitrary diameter calong the conical surface 78 and the end plate 80. The female element 52contains an air channel 82 which leads to and opens out of thecylindrical exterior surface 76.

The male element 54 likewise fits within the bore 66 of the base suchthat it can slide to and fro in the bore 66. It has an external conicalgauging surface 86 which leads out to its end and is presented outwardlyaway from the axis X, with the inclination of that surface 86 relativeto the axis X corresponding to the inclination of the tapered raceway 44on the cup 32 of the bearing B2. Moreover, the conical surface 86 issmall enough to fit into and contact the tapered raceway 44 for the cup32 of the bearing B2. At one point along it, the conical surface 86 hasa diameter c which equals the diameter c along the conical interiorsurface 78 on the female element 52. The male element 54 also has an endface 88 that is perpendicular to the axis X, and that end face 88 liesat a distance d from the diameter c of the conical exterior surface 86.

The two air channels 70 and 82 are connected to air gauges 90 and 92,respectively, which discharge air through the channels 70 and 82 tomeasure the gaps between the ends of the channels 70 and 82 and surfacesbeyond those ends. The channels 70 and 82 and their respective gauges 90and 92 constitute additional measuring devices.

The measuring device 56 is mounted on the end plate 80 of the femaleelement 52, and it measures the distance e between the end plate 80 andthe end face 88 on the other male element 54. Thus, the distance fbetween the corresponding diameters c along the conical interior surface78 on the element 52 and along the conical exterior surface 78 in theelement 54 equals the sum of the distances b, d, and e, that is to say:f=b+d+e

In order to install the shaft S in the housing H with the proper settingin the bearings B1 and B2, the cones 30 for the two bearings B1 and B2,each with its complement of rollers 34 around it, are pressed onto theirrespective bearing seats 6 and 14 on the shaft S with their back faces42 against the shoulders 8 and 16. Likewise, the cup 32 for the bearingB1 is pressed into its bore 2 in the housing H with its back face 46against the shoulder 4. Then the shaft S is installed in the housing Hsuch that the cone 30 and rollers 34 for the bearing B1 fit into the cup32 for the bearing B1. This supports one end of the shaft S on thebearing B1. The cone 30 and rollers 34 for the bearing B2 lie within thethrough bore 10 at the other end of the housing H. The gauge G is fittedinto the through bore 10 and around the cone 30 and rollers 34 for thebearing B2 to temporarily support the other end of the shaft G. The cup32 for the bearing B2 is fitted to the gauge G where it lies remote fromthe cone 30 and rollers 34 for the bearing B2.

More specifically, the cup 32 for the bearing B2 is fitted over theconical gauging surface 86 on the male element 54 of the gauge G andinto the end bore 64 of the base 50. Then the retainer 18 is attached tothe end of the base 50 to provide a backing for the cup 32 and preventit from escaping. The spring 58 urges the male element 54 into the cup32, causing the external conical surface 86 on the male element 54 toseat snugly against the tapered raceway 44 of the cup 32 and driving theback face 46 of the cup 32 snugly against the retainer 18. This,positions the back face 46 of the cup 32 in the same plane as the endface 62 on the base 50 of the gauge G. The cylindrical exterior surface48 on the cup 32 rests against the surface of the bore 64 diametricallyopposite the end of the air channel 70, leaving enough clearance betweenexterior cylindrical surface 48 of the cup 32 and the surface of the endbore 64 at the end of the air channel 70 to enable air to escape fromthe end of the air channel 70. That clearance should range between about0.18 and 0.25 mm (0.007 to 0.010 in.)

Once the cup 32 for the bearing B2 is installed in the gauge G, thegauge G is aligned with the shaft S and advanced over the cone 30 androllers 34 of the bearing B2 until the end face 60 on the base 50 isagainst the reference surface 12 on the housing H. When the base 50 isso disposed, the cylindrical exterior surface 76 of the female element52 lies within the through bore 10 of the housing H and the conicalinternal surface 78 fits around the rollers 34 of the bearing B2.Indeed, the spring 58 urges the conical gauging surface 78 snuglyagainst the side faces of the set of rollers 34, placing it within theconical envelope formed by the rollers 34. The cylindrical exteriorsurface 76 on the inner member 52 rests on the surface of the throughbore 10 diametrically opposite the end of the air channel 82, leavingenough clearance between the cylindrical surface 76 of the inner member52 at the end of the air channel 82 and the surrounding surface of thebore 10 to enable air to escape from the end of the air channel 82. Thatclearance should also range between about 0.18 and 0.25 mm.

Once the gauge G is installed against the housing H and around therollers 34 of the bearing B2, the shaft S is rotated slowly to seat therollers 34 of the bearings B1 against its raceways 38 and 44 and therollers 34 of the bearing B2 against its cone raceway 38 and the conicalgauging surface 78.

The distance b between the diameter c on the conical gauging surface 78and the end plate 80, both on the female element 52, is known, as is thedistance d between the corresponding diameter c on conical gaugingsurface 86 and the end face 88 of the other inner member 54. Themeasuring device 56 measures the distance e between the end plate 80 ofthe inner member 52 and the end face 88 of the other inner member 54.The sum of the three distances b, d and e equals the distance f betweenthe corresponding diameters c on the conical gauging surface 78 and theconical gauging surface 86, or, in other words, equals the distance of fbetween corresponding diameters c on the envelope formed by the outersurfaces of the rollers 34 and the envelope formed by the cup raceway44. That distance f less the distance a between the end faces 60 and 62of the base 50 gives the distance that the back face 46 of the cup 32for the bearing B2 will locate beyond the reference surface 12 if thecup 32 were installed in the through bore 10 without an interference fitand with the bearings B1 and B2, in a condition of zero end play (no endplay, no preload). The difference between the distances f and a is bestperceived by visualizing the diameter c along the gauging surface 78moved to a plane defined by the reference surface 12 of the housing H.This moves the diameter c along the other gauging surfaces 86—and alongthe cup raceway 44—to a position where that much of the cup 32 whichprojects beyond it is the amount of bearing lateral for which the shimmust compensate were there is no interference fit between the throughbore 10 and the cup 32.

However, the interference fit between the through bore 10 and the cup 32of the bearing B2 will cause the raceway 44 of the cup 32 for thebearing B2 to shrink, and that will increase the bearing lateral bydisplacing the back face 46 of the cup 32 an additional distance gbeyond the reference surface 12 on the housing H. The air gauges 90 and92 provide measurements for calculating the further displacement gcaused by the interference fit. In this regard, the air gauge 90discharges air through the air channel 70 in the base 50 and against thecylindrical exterior surface 48 of the cup 32 for the bearing B2, and ineffect, measures the diameter of the exterior surface 48 withconsiderable precision. The air gauge 92 discharges air through the airchannel 82 in the female element 52, and in effect, measures thediameter of the through bore 10 also with considerable precision. Fromthe measurements of the two diameters, one can calculate theinterference fit. Well-known formulas exist for translating theinterference fit and the shrinkage of the cup raceway 44 that it causesinto the displacement g of the cup back face 46.

Thus, the thickness t of the shim 22 which will provide the bearings B1and B2 with the proper setting in terms of a lineal dimension j reducestot=(f−a)+g±jThe dimension j is positive when the setting is end play and negativewhen it is preload.

Variations are possible. For example, the raceways 38 and 44 for thebearing B1 may be directly on the shaft S and housing H and likewise theraceway for the bearing B2 may be on the shaft S, thus, eliminating anyone or both cones 30 and perhaps the cup 32 of the bearing B1 as well.The measuring devices for the cylindrical surface of the bore 10 and thecylindrical surface 48 of the cup 32 for the bearing B2 may take formsother than the air gauges 90 and 92, for example, LVDTs. In lieu ofinstalling the spacer behind the cup back face 46 for the bearing B2, itmay be installed between the cone back face 42 for the bearing B2 andthe shaft shoulder 16. Indeed, the gauge G may be configured to select aspacer for directly mounted bearings B as well. Also, the shaft S may befixed, and the housing H may rotate about it.

1. A gauge for setting a pair of tapered roller bearings mounted in opposition along a common axis and between inner and outer machine components, one of which has a cylindrical surface to which a race of one of the bearings is to be fitted with an interference fit and also has a reference surface located at an angle with respect to the axis, said gauge comprising: a base having an end face configured to fit against the reference surface and at its other end configured to hold the race that is to be fitted to the cylindrical surface, so that the race is detached from said one machine component; a first gauge element mounted on and shiftable axially relative to the base and having a gauging surface for contacting a conical envelope on the detached race that is carried by the base; a second gauge element also mounted on and shiftable relative to the base and having a gauging surface for contacting an identical conical envelope on the bearing of which the detached race is also a part; a first measuring device for determining the axial positions of the first and second gauge elements to ascertain the distance between gauging surfaces on them; a second measuring device for determining the diameter of the race that is carried by the first gauge element; and a third measuring device for determining the diameter of the cylindrical surface of the one machine component, so that the magnitude of the interference fit may be ascertained.
 2. A gauge according to claim 1 wherein the gauging surfaces on the first and second gauge elements are tapered.
 3. A gauge according to claim 2 wherein the second measuring device is on the base and the third measuring device is on the second gauge element.
 4. A gauge according to claim 3 wherein the second measuring device includes an air channel which opens out of the base and the third measuring device includes an air channel which opens out of the second gauge element.
 5. A gauge according to claim 2 and further comprising a spring which urges the first and second gauge elements apart.
 6. A gauge according to claim 1 wherein the first and second gauge elements are located within the base.
 7. A gauge according to claim 6 wherein the gauging surface on the first gauge element is presented outwardly away from the axis and the gauging surface on the second gauge element is presented inwardly toward the axis.
 8. In combination with the gauge of claim 1, inner and outer machine components and first and second bearings for accommodating relative rotation between the machine components about an axis, one of the machine components having a cylindrical surface located around the axis and a reference surface located at an angle with respect to the axis, the first bearing including inner and outer tapered raceways carried by the inner and outer machine components, respectively, and tapered rollers organized in a row between the raceways, the second bearing including inner and outer tapered raceways and tapered rollers located along the inner raceway, the outer raceway and the tapered rollers defining identical conical envelopes having their axes coinciding with axis of rotation, one of the raceways of the second bearing being on a race having a cylindrical surface that is sized to fit along the cylindrical surface of said one machine component with an interference fit and also having an end face oriented at an angle with respect to the axis, the other raceway of the second bearing being carried by the other machine component, the tapered rollers of the first and second bearings being oriented in opposite directions, and wherein the base of the gauge bears against the reference surface on said one machine component and temporarily carries the race of the second bearing at a location axially offset from the cylindrical surface of the one machine component so that the two conical envelopes are spaced apart axially; wherein the gauging surface of the first gauge element bears against the conical envelope on the axially separated race; wherein the gauging surface of the second gauge element bears against the conical envelope that is on said other machine component; wherein the first measuring device determines the spacing between equivalent diameters on the two conical envelopes; wherein the second measuring device determines the diameter of the cylindrical surface on the race carried by the base; and wherein the third measuring device determines the diameter of the cylindrical surface on said one machine component; whereby the magnitude of the interference fit between the race of the second bearing and cylindrical surface on said one machine component may be ascertained.
 9. The combination according to claim 8 wherein the gauging surfaces on the first and second gauge elements are tapered and inclined at equal angles with respect to the axis, which angle corresponds to the angles of the conical envelopes.
 10. The combination according to claim 9 wherein the second measuring device is along the base and the third measuring device is along the second gauge element.
 11. The combination according to claim 10 wherein the cylindrical surface on said one machine component is the surface of a bore in the outer machine component.
 12. The combination according to claim 11 wherein the tapered rollers for the second bearing are around the raceway on the inner machine component and the second gauge element projects into the bore of the outer machine component.
 13. The combination according to claim 10 wherein the first and second gauge elements are located within the base.
 14. The combination according to 10 wherein the first measuring device measures the distance between the first and second gauge elements.
 15. A process for setting first and second bearings for accommodating relative rotation between inner and outer machine components about an axis, one of the machine components having a cylindrical surface located around the axis and a reference surface located at an angle with respect to the axis, the first bearing including inner and outer tapered raceways carried by the inner and outer machine components, respectively, and tapered rollers organized in a row between the raceways, the second bearing including inner and outer raceways and tapered rollers located along the inner raceway, the outer raceway and the tapered rollers defining identical conical envelopes having their axes coinciding with the axis of rotation, one of the raceways of the second bearing being on a race having a cylindrical surface that fits along the cylindrical surface of said one machine component with an interference fit and also having an end face oriented at an angle with respect to the axis and spaced axially from the reference surface, the other raceway of the second bearing being carried by the other machine component, the tapered rollers of the first and second bearings being oriented in opposite directions, said process comprising: placing the inner machine component in the outer machine component; eating the rollers of the first bearing along the tapered raceways for the first bearing; locating one of the conical envelopes for the second bearing on said other machine component; axially separating the other conical envelope and the race of the second bearing from said one conical envelope; measuring the axial distance between equivalent diameters on the separated conical envelopes; while the conical envelopes are separated axially, measuring the diameters of the cylindrical surfaces on the race and on said one machine component; installing the race along the cylindrical surface of said one machine component; from the measured axial distance between equivalent diameters on the separated conical envelopes and the measured diameters of the cylindrical surfaces, calculating the thickness of the spacer which, when fitted against the reference surface on said one machine component, will provide the first and second bearings with the desired setting. 